Better efficiency, some yes, but a thermal storage tank will give you more convience, sized properly.
I have a square tank design, check out my signature. I've been very impressed with the hx coils, and the overall tank. It was easy to set up in my basement. The company was good to deal with. I was able to go about 5 days in the summer, on 1 fire, thats with 3 teens, etc. It has good holding power.
With baseboard heat, you might have to fire more than once every 24hrs. But I have 1800sq/ft 2 story house, on top of a hill on northern maine. Moderate insulation. With 3 kids taking showers in morning. Also, my house looses heat quicker than i would like. Yours is a 2003 it should be tighter than mine. It's been close to the single numbers in the am. 1 big fire a day seems to hold me. I build a fire about 4pmish, if it's needs more heat later, i refill boiler while it's still burning. I have baseboard heat in house, but i also have staple up radiant floor in my kitchen. This helps me a lot. Able to get better use of my tank with radiant. Eventually will do the rest of the downstairs with it. Maybe low temp radiators up stairs, when time/budget allow. That's going to be the key to this set up. Plus I would like to dump another foot of blown-in insulation in the attic. Do some other upgrades. I'm heating my house on about 7 cord of good seasoned hardwood. Thats year round, including my DHW.
This is the place for your questions. A lot of good people here, great experience and willing to share. BUT you need to do a heat load calc, if you haven't done it already. This will help enormously! I'm not sure which ones the best, but someone will suggest a few to use.
If you don't do it already, little things like setting back the thermostat at night helps. We turn the t-stat back to 62/64 at night. During day, house stays about 68ish, maybe a little warmer. If no ones going to be home all day, goes back to 64. With baseboard, I get a quick blast of heat when i fire up my wood boiler. Got home last night and tank was down a little more than usual. It was in the 102/105 range. It took me a load and a half to get the house and tank back to temp. But, wife was cold, t-stat in house was set at 74, plus all other zones were calling for a little heat. A lot of demand.
Do your heatload calc! Imprortant to figure what you need. How many times do you fill the unit during the day? Have you been burning since 2003?