I think the new site is better... though you may want to remove the advertising at a future point.
"There is lots more information on this site, so please feel free to look around. I welcome enquiries by telephone or email and you are of course very welcome to arrange a visit."
No telephone number, no click through on the word email. I would add those to that page... just to make it really easy for someone to contact you.
The page title appears to be Home. I've looked at the Webs.com system and I can't figure out how to change that without it affecting the Menu names. It's a limitation of the system... bit of a pain.
If you decide to go with the Webs.com system, make sure you put things in the Site Description and Keywords boxes, located in Site Settings.
For example a description could be: Catherine Campbell - Childminder in Stanningley Road, Bramley Town, Leeds LS?? - Providing daytime childcare, before school, after school care.
LS?? is where you put the first part of your postcode. So if someone searched for: childcare LS20 if you were in LS20 you would appear on the search listing.
Bottom of Services page contains some generic text that needs to be removed, as does About Me. Best to check all pages to make sure the text from the initial template has been removed.
Put some more information in the footer. For example key phrases that parents might search for, which are relevant to the content of your site: Childminder in Leeds providing care for babies, toddlers and school aged children.
I wouldn't bother with Links, Guestbook or Calendar. Especially as you are linking to NetMums and not MumsNet
The font on the Working with Parents page looks different to the font used on the other pages. Try to keep things consistent.