Tables are read left to right, top to bottom. Let's take seasons 4/1 in the first table for example. Those numbers are read as: Buffy 4x01, Angel 1x01, Angel 1x02, Buffy 4x02, Buffy 4x03, Angel 1x03, Angel 1x04 and so on. If you watch series from DVDs, use printable episode list instead: there are no episode numbers in menus, only titles. They are organized so poorly that you may need such list for all seasons, not just 4/1-7/4. There is no printable version for second table, only a plain text list.
First three seasons of Buffy happen before Angel storyline, so they should be watched first. Also, the last season of Angel happens after Buffy events.
4th and 5th Buffy seasons were shown back-to-back with first two seasons of Angel, so it's natural to think that it should be correct watching order. However, there are some episode pairs in both series that share one storyline, all of them are shown in the second table.
My opinion is to separate Buffy and Angel when watching them would be the best way, because those series are different in atmosphere, and to mix them may result in ruining impressions from either Buffy and Angel. So I've compilated the first table so episode packs are the longest without giving away spoilers and missing crossovers.
6th season of Buffy and 3rd Angel season have no crossovers. But it would be right to watch a couple of Angel episodes first to watch Angel's reaction to last season's finale. Also, there's a slight cliffhanger in 3x02. There is no point alternating series every episode this season, because storylines often span 2-3 episodes and it's easy to lose touch with events. The same goes for next seasons, thus the second table for seasons 7/4 is only one line longer.
Next season watching order is completely messed up :-) Buffy somehow got ahead of Angel, so two major crossovers are among 7x17-4x15-7x18 and 4x22-7x21. My friend mentioned that it's better not to split Angel's 4th season to not ruin impression, so I recommend following the first table: there are no serious crossovers in first 15 episodes.
Comments above are mostly related to the second table. After lokapala showed up in my LJ, the first table (the preferred one) has been shortened badly. You can see the result of her advice not to interrupt 3rd and 4th seasons of Angel with anything (not ever food and sleep! :) Now you need to worry about switching discs only for two (four?) seasons.
If you have further comments, please write them here.
SSJConan from Wikipedia for compiling the recommended order of viewing the intertwining season episodes. That page was of great help polishing the second table. Also, there are links to each of 254 episodes of both series complete with airdates and short descriptions mentioning crossovers. That is so great, too bad it doesn't fit into Wikipedia content rules. In case it's deleted, I've backed the list up here.
Matt Naglieri and Chris Everett from Home Theater Forum. Their posts were my first source of information.
Some random person who compiled a list at Amazon.com with recommended viewing order for 7th/4th seasons. I'd gave it some thought but didn't use it in the end. But there was a note that 4x14 comes before 7x17 which I used, although it contradicts wikipedia.
Mary (lokapala) for a great help polishing the first table. Now it's almost perfect. This order is mostly hers, with my minor corrections and design :)
My friend Fitzgerald for a great advice not to interrupt 4th season of Angel with Buffy storylines. And for mentioning the difference between series, which led me to reducing the first table as hard as I could.
And my friend Donna for convincing me to start watching Buffy. It's one of the best series I've seen in my life. Thank you again.
Special thanks goes to Julia, my girlfriend, because of whom I get to watch Buffy for a second time, now with Angel :-)
Last modified 11/24/08: seasons 4/1 begin with Angel, fixed wikipedia link.