Note: Both variations of our Land Raiders can transport units as well, but I'll be doing those in the Heavy Support article.
Rhino:
Ah, yes. The humble Rhino. It was the key cog in many of our lists over the past few years, providing our relatively fragile units protection and mobility. While it remained somewhat pricy compared to the newer 5th Edition codices, it was a vehicle that you couldn't leave home without. Having the ability to maneuver around the battlefield was that important, and honestly, it still is.
There have been some changes, however. Gone are the days where you can drop close combat-oriented troops from normal transports. In case you're not familiar with the rules, that is due to not being able to assault the turn you disembark from your transport (unless its an assault vehicle). In addition, a disembarking action cannot be made if the transport moved more than 6" in that movement phase. Kind of a bummer right? Well, if it makes you feel any better, every other army has to deal with this "nerf" as well.
So gone is one of the huge reasons for taking transports. But are they still useful? Absolutely! They still give us protection and mobility. These are things that will probably become even more important going forward in 6th Edition. Objectives are going to be harder to reach, more plentiful, and there are more mission parameters. Your troops will be very important in claiming objectives/table quarters, so will require as much time out of the line of fire as possible. Just remember that you have to disembark to "claim" those objectives, as your troops don't count as scoring while embarked in a transport.
There is an argument regarding whether or not Rhinos are worth taking due to the changes in vehicle damage. Some players believe that vehicles are easier to kill due to the Hull Point additions and the increased ability to strike them in CC. I would agree, if you're talking on the scale of a single vehicle. Its quite easy to focus and destroy a Rhino. But if you have 6, plus other vehicles on the board? I believe that the redundancy actually makes it harder for you to be de-meched. It ultimately comes down to the fact that vehicles died just as fast in 5th Edition when my opponent wanted them to, so there is no difference to me now that there is a new edition. A skilled opponent will destroy my vehicles no matter what, so there is no use worrying about the how it happens. Stelek talks about this a bit in his article here.
But of course, its not all bad. Its easier to grant cover saves to vehicles now, allowing simple infantry or small-scale terrain to provide 25% coverage. Area terrain now grants cover to vehicles. Transports can make an extra "flat-out" move in their shooting phase, but it prevents their occupants from shooting. Sometimes that extra little push is needed. And then there is the ability to fire heavy weapons from moving transports using the Snap Fire rules. While you only have a 1/6 chance of succeeding, that is a significantly higher percent chance than what we got in 5th Edition. This makes them perfect for transporting units such as MM Bunker squads around. In addition, they can still tank-shock, though its harder to pull off due to the changes in Moral. And let's not forget their usefulness in providing mobile cover for your forces or LOS blocking "terrain" for your units in key positions.
So in the end, are Rhino's useful? Definitely. Especially if you use them with shooty squads. They are much less needed if you intend to outfit your squads in a CC-oriented manner. In fact, I wouldn't advise giving them a Rhino-chassis transport at all. However, because of the expensive nature of our troops (and our need to have many of them), smaller squads stand a much better chance at survival if they use our boxes. While these vehicles provide very little in the way of firepower, they will be important going forward for the same reasons as they were in 5th Edition.
Razorback:
The Razorback has almost all of the of the pro's and con's that the Rhino has, with a few extra on top. Previously, the main reason for selecting a Razorback was its ability to fire a heavy weapon. This will still be the case, but its less needed for it's anti-tank duties because I believe that people (at least initially in knee-jerk fashion) will be taking fewer vehicles in their armies. On top of that, I feel that torrent of fire is the way to go moving forward (or highly effective AT), so having a larger array of weaponry is going to be important. Right now, all the BT Razorbacks can take is the standard TL-Heavy Bolter and the TL-Lascannon. The first isn't very good period, but the latter doesn't fulfill the ToF that we're looking for.
In addition, your Razorback has no fire points so an embarked unit cannot fire. Because your embarked unit won't likely be a CC-oriented squad due to the changes in transports, they'll either be a shooty unit or naked. Having no fire points is a big problem for the former. Combine that with a very expensive price tag, and you will be seeing fewer of these on the board. Now, if we get updated in line with the rest of the SM Chapters? Then my statement will need to be adjusted.
All is not lost for the Razorback though. It is still one of the best sources of long-range weaponry in the Black Templar codex, even at the price of 90 points. Shooting has only gotten better in the new edition, so these will still have a place in some armies. With proper application of points, you have the ability to field more long-range weapons in your army than almost anyone else in the game. In addition, you can still add a Power of the Machine Spirit upgrade to the vehicle, but with the new vehicle damage rules, I don't think that its wise to invest 120 points into an AV11 vehicle any longer.
Moral of the story: Razorbacks are useful for gunline armies or units designed to camp home objectives.
Drop Pod:
Disregarding the fact that Games Workshop accidentally removed the ability to even take a Drop Pod, there have been some big changes to them. The big one is regarding how they come down from reserves. As predicted, we lost our ability to stay completely in reserves and with it, our ability to use board manipulation. However, with the changes to the die roll needed to bring out units from reserves on turn 2 (6th: 3+; 5th: 4+), we don't get slammed by the piecemeal drops nearly as bad. Thus, drop pod armies will still be a viable strategy going forward. It, however, does have a flaw in 6th Edition that can't be dealt with without ally support: Flyers.
One of the benefits of drop pods is the ability to deliver Alpha Strike forces into your opponent's army on turn one. Against a skilled opponent, they will be ready for this, but much like the DDP of 5th Edition...it allows you to control the tempo of the game early on. You give yourself the opportunity to cripple a portion of their army, but it will cost you that unit in reply.
Likewise, with the close combat nerf to transports, drop pods may see a rise in that respect. They are a good way to deliver CC-oriented units to where they need to go, early on in the game. Because they have to wait a turn to charge anyway (due to the new transport rules), all they have to do is survive the shooting phase and you're off to the races. They are able to drop with relative accuracy, anywhere on the board. This has obvious strategic and tactical advantage, especially when used in conjunction with your troops. The ability to reliably land on objectives or in specific quarters is huge. And it doesn't rely on your opponent's shooting, or lack thereof, to accomplish that goal. The only real hindrance is Warp Quake.
On the other hand, drop pods come down immobilized. Thus, in some tournament scenarios, that will cause you to lose Victory Points right off the top just by dropping. They are still relatively easy to kill, being open-topped, and don't really provide much in the way of firepower. Then we have the problem of mobility after the drop. In a non-board manipulating army, you'll need to go to where the enemy is. But if they are faster than you are (i.e. Necrons, Dark Eldar, Eldar, SM Bikers, etc), then you're going to have problems. You won't be able to get to where you need to be in a timely manner and you'll just get picked off slowly.
Despite that, the drop pod is a very viable replacement for the Rhino. Just remember that your army's redundancy is affected and you are forced to deploy 1/2 of your drop pods on the first turn. Its best to ensure that you either have a CC-oriented unit embarked or one that can cause some serious Alpha Strike problems (i.e. Command squad) if you're bringing it down in the first wave.