What did they do with the game settings, this is not the game I played in the 90s... In ANY difficulty setting it is impossible to play when you're against the gray's. I lose 8 to 10 of my soldiers because they panic, get under control by aliens and shoot their fellow soldiers... Sometimes I cant even make it to the entrance of a crashed UFO with 1 soldier... they're all dead within 2 of 3 turns... Frustrating ...

Or maybe you're just rusty at tactics.

Give OpenXcom a whirl and maybe practice the tactics in Battle Mode.

I've seen several Let's Plays of X-Com recently, and they've taken a cautioned approach. (It might be you were playing the broken version that accidentally set the flag to easy while GOG uses a fixed version.)

I started the game a few days ago with OpenXCOM patch/mod and on my third mission it was exactly just that: a terror mission with psionic sectoids and about 5 cyberdiscs. I barely made 4 laser pistols by the time and no armor (or armour if you prefer) and you know what? I made it, I had to rush 4 soldiers to kill the closest psionic (there were at least 2 active) with common weapons while laser squad (hmm... sounds familiar) and heavy cannon + missile launcher soldiers dealt with cyberdisc in vicinity.

3 months later and no psionics still. Thank goodness. And I've watched a couple of Let's Play videos on Superhuman and no one get psionics so earlier. So I guess it's all about luck. I almost done with personal armor and laser research soon they'll deploy chryssalid, ugh...

Playing on Genius difficulty because I'm no superhuman ;)
This game is better than XCOM: Chimera Squad in every way and since there are no more XCOM left I decided to complete the original series.

I too have terror on third battle. And im failed. :( Have squad with tank (heavy) and all rest ship is humans - full ship. Tank destroyed by enemy "vehicles". But my soldiers almost win then. Some two (or maybe even just only one?) aliens always mind controls my remained soldiers or my soldirs (some with wounds) are panic each turn. I failed when alien(s) kill two of my... bravest... soldiers and some 2-3 alive keep mind\panic (form when i cant control them). Im not sure about details. I skip game in that difficulty on that moment.

I researched last aircraft, all laser and plasma tech, most of alien tech, haven't yet touched alien food and surgery (entertainment was *very* useful), done all autopsies except for sectopods and slimes thingy (not encountered them yet), I have captured alive medic, navigator and a snake leader (mind probes for the win). But the last fight was a complete disaster I decided to trace the large UFO till it lands and when my troops all wearing power suits went on I saw an ethereal leader right outside my ship, I thought great I can capture him, maybe get some psi tech, he ate 3 *sleep* rockets from small launcher and he didn't even twitch but I was able to get him unconscious with lucky laser hit, I placed one gut with a stun rod protecting the body, but since I pressed the end turn the nightmare begins: constant psi attacks, 3-4 were instantly persuaded to serve the great alien cause, I threw a grenade and killed couple of good soldiers, but I managed to kill all ethereals in the end and it was a massacre...