I just played/finished SR and I loved the atmosphere & the combat. Very linear story with my choices meaning very little (if anything), and I can't understand why I shouldn't be able to loot my enemies for their weapons/armor (only very select plot point drops). But whatever, I still enjoyed it very much.

So now I just started Dragonfall, and I can't even get through the end of the first mission (TPK twice, and escaped once but didn't keep the entire team alive).

I had both games to Normal difficulty, and I only failed missions twice in SR (and those were both very near the end of the game).

Anyone else notice an increase in difficulty with Dragonfall? I'd rather not set the game to Easy, but it beats failing 3 times in a row on the very first mission.

I recently replayed every SRR game on hard (face (I really see no reason not to pick as much etiquettes as possible - the whole game is ,ore enjoyable as a quest with tactical combat elements rather than other way around, if you ask me) + something other than my standard decker + pistol/cyberweapons pick) and, IMHO, the hardest part of them all was not dying from boredom in the hive sequence in DMS. )
Your problem seem to stem from the fact that the whole armour, cover and crit mechanic has been reworked: DF and HK *really* want you to stay in cover. Hit the deck. Stick to that semblance of a shield and pray that these psychos with kitchen implements won't force you out into the shower of lead. While almost every character (well, sans those that have less than 2-3 points in body - they just aren't cut for shadowrunner life) is reasonably sturdy even when in half-cover, most models will kick the bucket out in the open: even at low levels of proficiency crits aren't that uncommon - it's the accuracy that will need to be buffed most of the times. So, flanking, flushing enemy out from the cover - and then zeroing in on the enemy is the name of the game. Probably just some change of your tactics is in order.
To add to that, you could also be just a bit unlucky: AFAIK, SRR does not use your standard probability adjustment so prevalent in a lot of strategy and tactics games, so the random is at least somewhat 'real'.

Thanks for the tips, Dition (or should I call you Harcourt Fenton Mudd?). I had no idea the mechanics were tinkered with.

I was able to get past that first mission by using not only your cover suggestions, but also by finding a walkthrough on GameFaqs that told me where the enemies were coming from & who to focus my fire on.

Got through a couple more missions, no more dead party members thanks mostly to using cover. Thanks again for the tip!

The fight sets the mood for the game. I have only ever come close once to killing the boss, and that was before I realized that the point of the fight is to survive and not to kill everyone. Just run and hide until the escape is available and then get everyone out. (Kill the weaker opponents, for sure, otherwise survival is that much harder in a cross-fire.)

There is a big mission later on, just before the end railway, which is both a timed escape and a difficult stealth set-up.

Also, the first part of the end, when you are fighting in a(nother) basement, is particularly difficult (and has a dilemma that changes some of the the ending).

I enjoy a game when the developers "talk" to the gamer; there are often hints. In this game there are clues in conversations that lead character development. You will see, except for a single instance* that I can recall, a threshold without which attribute a conversation option is not available; if possible — and consistent with whatever role play you have — it is rewarding to follow these bread crumbs. (This is deliberate; other UGC mods have both hidden requirements and visible failure, to indicate what is needed to have an option available, which is much friendlier.)

But I agree the difficulty is higher. The entire endgame — you'll know it when you start it — is more difficult than anything else in the official campaigns, except the extra levels of Hong Kong, which are designed for advanced characters with nine-plus ranks in their main attributes.

* There is a hidden requirement for minimum intelligence of three (scilicet, an IQ of 100) very early on; I can rationalize this as the minimum apperceptive limit beyond which a PC can pick up such conversational cues. :)

edit for clarity.