I can't help at all with regards to Abu Dhabi as I don't know the place, but for those coming to Dubai, here's a run down on the bars:
Old Dubai (Bur Dubai)
Yesterdays - Four Points by Sheraton Downtown Dubai (Mankhool Road): Traditional English pub
The Music Room – Majestic Hotel (Mankhool Road): Big bar, live rock music, 4 pool tables
Barrels – Majestic Hotel (Mankhool Road): Small, quiet sports bar
Jockeys – Panorama Hotel (Mankhool Road): English pub with an 'interesting' clientele
The Old Vic – Ramada Hotel (Mankhool Road): Traditional English pub
Goodfellas – Regal Plaza Hotel (Mankhool Road): Sports bar
Johnnie's – Sea Shell Inn Hotel (Khaled Bin Waled Street): Small bar with pool tables
Waxy O'Connor's – Ascott Hotel (Khaled Bin Waled Street): Irish pub. A Dubai institution on Fridays. Cheap drinks deals 12-7pm. Very lively. Like walking into a nightclub after 5pm.
The Viceroy – Four Point Sheraton (Khaled Bin Waled Street): Traditional English pub
The George & Dragon – Ambassador Hotel (Al Falah Street): Traditional English pub (very cheap)
(The above are all within walking distance of each other and make for a good pub crawl)
Rock Bottom – Regent Palace Hotel (Trade Centre Road): Bar/Nightclub, lively after 10pm.
The Players' Lounge – Country Club Hotel (Port Rashid Road): Sports bar with live band.
The Mariner's Club - Sea View Hotel (Mina Road): Live Filipino rock band (ACDC etc). 'Interesting' clientele.
The Irish Village – The Aviation Club (Garhoud): Big Irish pub, great food, HUGE beer garden. Very popular.
Chi@The Lodge – Al Nasr Leisure Land (Lamcy): Huge 3,000 capacity open-air nightclub. Indie, Dance, R&B. Very popular, expensive.
Sheikh Zayed Road (City centre, in between old and new Dubai)
Long's Bar – Towers Rotana (SZR): Large English/American bar.
Double Decker – Al Marooj Rotana (SZR): Huge English pub. Very popular on Friday afternoons. Beer garden. Food/drink offers.
Harvester's – Crowne Plaza (SZR): English pub. Home of the rags, so avoid at all costs.
Zinc – Crowne Plaza (SZR): Nightclub popular with Emirates Air Hostesses.
Fibber Magee's - Behind Crowne Plaza (SZR): Cracking Irish pub. Great food and great atmosphere.
The Red Lion – Metropolitan Hotel (SZR): Traditional English pub. Good food. Beer garden.
Rattle Snake – Metropolitan Hotel (SZR): Live music. 'Interesting' clientele.
New Dubai (Barsha, Marina, Palm, Jumeriah)
The Crown & Lion – Byblos Hotel (TECOM – Al Barsha): Large, modern English pub. Loads of big screens (this is where the City Supporters Club meets for games), pool table, dart boards.
Barasti – Le Meridien Mena Seyahi (Marina): Large, modern, open-air beach bar. Very popular. BBQ on Fridays.
The Locker Room – Golden Tulip Hotel (Barsha): Large, dark sports bar. Very cheap all-you-can-eat/drink deal on Fridays from 1pm til late.
Bidi Bondi – Shoreline Building 3-4 (Palm Jumeirah): Aussie-themed sports bar. Large outdoor terrace.
The Underground - Habtoor Grand (Marina): Sports bar. Home of the red bin dippers.
That should be enough to keep all you alcoholics happy. Bars are open midday-3am. Nightclubs are 10pm-3am. I particularly recommend the ones in bold if lively, busy places are you thing. Enjoy.