As I recall, AGM can deliver high current pretty well too. A 3 kW load on the inverter is about 290 amp draw on the battery (figuring 85% efficiency in the inverter). That's 1.28 C on the T105 bank vs 0.85 C on the AGM bank (*see footnote). I think the AGM would be better able to handle the peak draw from the inverter. However, again just winging it on memory.. it seems like AGM should not be allowed to reach the same depth of discharge that the T105 can tolerate. Whether the larger AH versus less discharge tolerance nets roughly equivalent available power, I don't know.
3 kW is a fair amount of power. It probably makes sense to have headroom in the inverter and wiring to support it, but it may be uncommon to actually draw that much for any length of time in practice. The AGM superiority at providing that much power may be irrelevant.
Why two separate 12 volt house battery banks..? I mean, I get that this is what you already have on hand and that it's not ideal to put that set of dissimilar batteries into a combined bank, but it kind of looks like a scenario where you'll create headaches for yourself by having separate banks with different battery types. If it's within the realm of possibility, maybe consider trading one pair so you can have a single bank of similar batteries.
footnote: "C" is battery terminology; it represents the AH capacity of the battery bank. In general, as the discharge rate in C goes down, the total power the battery can provide, seen as the length of time it'll power that load, goes up.