I main Engi but have a moderate amount of experience with Ele too. I mostly play WvW.
If you’re looking for team support (offensive or defensive) in WvW, Ele’s are always welcomed for their water fields, might stacking, and heavy AoE pressure (staff). Either one can roam effectively in WvW. I don’t play enough PvE to make recommendations there.
In my impression, the biggest difference is how Ele and Engi’s toolboxes are set up. Both professions have a large number of skills/versatility. Ele’s come in very large packages (20 weapon skills on a weapon set) that are relatively rigidly-defined (e.g. all D/D Ele’s will, of course, have exactly the same 20 weapon skills). Engi’s toolboxes are often smaller (unless it’s a 3+ kit Engi), but is more flexible. You can mix and match any weapon sets (kits/utilities) you like to fit your intended role/playstyle. However, in my impression, each individual Engi skill seems to have a little less impact than single Ele skills, perhaps because you can combine them in almost any way you like.
Finally, in terms of capabilities, Engi is pretty much the top profession IMO in terms of hard CCs, with lots of access to knockbacks and launches. They are also very strong for condition builds. Weakness are lack of stability and poor condition removal. Ele’s can put out a lot of healing and boons for teammates without giving up on personal offense or defense. Someone with more experience may be able to explain their weaknesses better than me, but I think it is mostly tied to their low health pool and armor, which may necessitate more defensive gear, traits, or utilities, to boost survivability.