I'll give a rundown of what I see in a couple I've known for many years and my own marriage, which happen to be the Betas you asked about. Hopefully some of it answers what you're looking for.
IEI + SLE - spend a lot more time together in leisure as a couple. They share more of the same interests and pursuits. They are also more carefree, fun, and laid back, or at least are this more readily and more often. Kicking back is more of an integral part of their lifestyle. They are more spontaneous as well, having guests over or dropping by as a guest with not much fuss. They do a lot backyard BBQ get togethers and impromptu pull-up-chair and have a brew type of socializing. While their work is important to them and their individual interests are there as well, those things take a back seat to "couple time". It's the reverse for EIE + LSI. IEI + SLE take time off easily and aren't fussy. They like to not worry about how much things cost. While, not spendthrifts, they are also not wallet watchers, which EIE and particularly LSI can be. Affection-wise they are more warm and demonstrative and openly solicitous to each other than the EIE and LSI are. They support each other by being very much on the same page. As far as I know from knowing them for 20 years, they agree on pretty much all the important things in life.
EIE + LSI - don't spend an awful lot of their leisure time together as a couple. They are more individuals. Both are very focused on their own career or pursuits and while they support each other, they tend to compartmentalize their various life parts much more than IEI and SLE do. Leisure time is for the most part also spent in individual pursuits. For example: He plays golf, in a sports league, poker with the same group, and goes to major league sporting events. She is in art classes, language class, goes on shopping trips, or scenic road trips. But, for the most part they don't do these together. Often it's with other people who are more into the particular hobby seriously or it is work-related. They don't kick back as easily. Tend to be more particular and fussy (judging, high maintenance) about how and where they spend their time. By the same token they can also be finicky on how they spend their money. They like to plan things out more in advance. Affection-wise EIE and LSI are more reserved and private. They support each other by acceptance of each other's drives. This is a pretty driven couple. They may not agree on everything, but they respect each other immensely. I think the support is derived from that sense of mutual respect.
How they started:
SLE woo'd IEI in the most traditional, forward, romantic way - flowers, chivalrous, etc. IEI female sees him as her White Knight.
EIE took supposedly reluctant LSIs hand and insisted he get up on the dance floor with her and the rest is history.