US shares can be more active than UK shares, they tend to have a higher volume, and you have more companies to choose. You will find a more excellent range of share price too. If you trade in the UK, you will typically buy shares from just a few pence up to £20 or so.
On that, be careful when purchasing shares in pence range due to their volatility. US shares, on the other hand, range from several hundred dollars to cents. Normally we would not consider a stock below $10.
Remember, the share price does not reflect the value of the company. The Brits seem to prefer a lower share price.
But holding ten shares in a US company and 100 in a similar UK company has no advantage or disadvantage for you other than the feeling of holding fewer shares. If the share price goes up or down, it is still going to have the same relative effect on your fund.