Q: is it no difference? Assuming two identical twins are managing the 2 funds with the same strategy.
A: different.

Imagine the old fund manager is holding some very toxic assets (perhaps some energy stocks). She dare not liquidate them for fear of realizing the loss. Now, suppose you invest $10k. Your “fresh” fund might be parked in cash (or some unusual, questionable hedge) because her top priority is protection of her existing (dangerous) positions. Also if the fund has suffered losses the ensuing redemption by other investors may force her to take unfavorable trades such as but not limited to forced liquidation.

In contrast, the $10k you put into a new fund is likely to be invested in a brand new “strategy” with no baggage.