gear questionFollow

So lets compare and start with the most easy one:

Gauntlets of Desolation: 32ap; 17crit rating; 2red sockets (assuming 2x8agi) = 48ap, 25crit rating = 1.25%crit; 48ap
Handguards of Precision: 20agi; 38ap = 0.5%crit; 58ap
By trading 0.75%crit for only 10ap Gauntlets of Desolation are the clearly better item.

Next two:
Beast Lord Cuirass: 30agi, 40ap, 4mp5, 24int, 2red, 1blue (socket with 2x8agi and 1x4agi/6sta for the socket bonus -> 24agi from gems and socket bonus) = 54agi, 40ap, 4mp5, 24int = 1.35%crit, 94ap, 4mp5, 24int
Bonechewer Berserker's Vest: 14agi, 72ap, 4mp5, 13int = 0.35%crit, 86ap, 4mp5, 13int.
Here the Beast Lord Cuirass is a ton better. You get 1% of extra crit, 8ap, 11int and don't loose anything...

And the next...
Auchenai Bracers: 36ap, 4mp5, 15int, 1red (assuming 1x8agi) = 0.2%crit, 44ap, 5mp5, 15int.
Lykul Bloodbands: 18agi, 30ap = 0.45%crit, 48ap
This one is really close. It is deciding whether to get 0.25%crit and 4ap over 5mp5 and 15int. If you can sustain your damage through boss fights I'd take the Lykul Bloodbands, if you constantly have mana issues go for the Auchenai Bracers.
Although you might just want to buy some PvP bracers as those have really solid stats:
Vindicator's Chain Bracers 23agi, 11crit rating, 24ap, 13int, 1yellow (assuming a 8crit rating gem) = 30.5crit rating, 47ap, 13int = 1.5%crit, 47ap, 13int.

The thing which you seem to have problems with when comparing items are those nice sockets. Don't underestimate their value.
Another thing which helps when comparing items is to know how to converse those values.
1agi = 0.5crit rating + 1ap
41agi or 20.5crit rating = 1%crit