Which speaker is better for an application based on it's datasheet
It might be slightly less bad but the ratio between maximum excursions is only 1.6, giving you 4dB more (potential) volume - barely perceptible.

You'd be better off either moving to a larger radiating area - a bigger driver (a 4 inch woofer is an oxymoron!) - look for one whose output doesn't roll off before the bottom of the band of interest.

Or if you can't afford the space, perhaps a tuned port to augment the output around 100Hz. Port tuning can be tricky, but there are loudspeaker enclosure design programs that will help. You're probably looking at an esclosure volume of about 4 litres with a fairly small diameter (25 or 30mm) port as a starting point.

Alternatively : is the speaker being driven outside its linear range by frequencies below the band of interest? Perhaps a high pass filter set to 80Hz will pass all frequencies of interest but protect the speaker from high amplitude 20-50Hz signals that can only drive the cone out of its linear range and potentially cause damage.