IG vs LatD, tough one..
I've played against both, and my thoughts are..
Leaders:
LatD have access to some great leadership.. Okay, they can't take a chaos lord. But for the role and scale of the army, an arch heretic or aspiring champions are well worth it.
These guys have access to the chaos armoury, probably the best armoury in the game, and can become terrifyingly nasty. Better still, they have ridiculously high leadership meaning that sticking an aspiring champion with the mark of chaos undivided in your mutant squad is liable to make them very difficult to break.
Guard leaders are not that inspiring, as things go. They are more about strategy than big shiny swords, though they can be quite surprising in that regard. Using vox caster upgrade, your commander can lend his considerable leadership to your entire army, and his command squad can be quite flexible in its equipment options. All in all, he has a powerful role in the army structure, and will hold it together, but isn't going to be taking down bloodthirsters any time soon.
Infantry:
LatD have a number of strategic options. Here are a few I can think of.
1. The mutie route! Large numbers of footslogging mutant infantry who charge across the board and hope some of them make it into close combat. My favourite!
2. The sneaky route. Lots of infiltrating traitors (always infiltrate traitors.. you're paying enough for the ability) who ambush the enemy with heavy weapons, or swamp them in CC (traitors are a good deal more flexible than their guard counterparts.)
3. The allied route.. Abseloutely min out your basic troops choices, then get lots of CSM allies to support them. I don't think it fits the style you're supposed to play with LatD myself, but nothing to stop you. You get access to some of the toughest troops in the game, and you should have a nice disposable meat shield to hide them behind. This alone is an extremely powerful combination.
4. A balance of the above. Probably the best, overall.
Guard are a lot more flexible due to their use of doctrines. There are a huge range of styles and army times, from infiltrators, to drop troops, to heavy infantry grenadiers, to mechanized infantry. It'd be silly to try and list them all here, but IG infantry generally revolves around the application of massed static firepower.. Lots of heavy weapons, lots and lots of troops to hide them amongst. The more troops, and the more heavy weapons, the better. Don't expect guard to charge into CC.. it can be done, but there are other armies who are far better at it.
Armour:
Now here's where it gets fun..
LatD are more based on infantry than armour, it's fair to say. But as has been mentioned, they get two of the most popular choices, the Leman Russ, and the Basilisk. They also get the defiler, which, although it looks cool, is generally considered inferior to the Basilisk. This armour is really just intended to support, I feel.. it will never be the thrust of your army.
On the other hand, armour in the IG list is very cool and important. It compensates for some of the biggest weaknesses guard have, such as their vulnerability to anti infantry weapons. They also get access to the demolisher, which is a very fun tank which helps to rectify the guard's weakness in offence. Tanks bring durability, flexibility and massive firepower to the otherwise all too human IG list.
This is a gross generalization, but I hope others agree with me that it's fairly accurate.