I've done both... and yep. The interaction is VERY different.
Take a standard working day (obviously there are a gazillion and 1 variations on this... this is just one example):
- Morning madness
- Drop off at childcare
- Pick up at 5-6pm
- Bedtime at 8pm
_______________
2 hours a day (not including morning madness)
SAHM schedule:
- Up at 6am
- Bedtime at 8pm
________________
14 hours a day
Now... working parents tend to CRAM in quality time during their hours off, so it can LOOK a lot more interactive (many working parents "do something special" either every day, or every weekend)... but it's a byproduct of time.
When you have a 14 hour day, you spread things out more, and aren't as "HAVE TO DO THIS!" as when you only have 2-3 hours a day. Also, things get "counted" differently. When you only have 2-3 hours and you have to cook, and you have your kid help / are talking about the day/ etc... that often gets "counted". For good reason. But stay at home parents often don't count that time, even though it's the same interaction.
It's not the same... but that doesn't mean one is better or worse. Just different. And, as always, what is MOST key is the personalities/individuals involved. You can be a VERY involved/ fun/ loving working parent, or a totally disconnected working parent. Or vice versa. It's less how MUCH time you have, and what you do in the time you DO have :)